The field of this invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to a method and apparatus for reducing noise in a three dimensional data array generated using magnetic resonance imaging techniques.
Any nucleus which possesses a magnetic moment attempts to align itself with the direction of the magnetic field in which it is located. In doing so, however, the nucleus precesses around this direction at a characteristic angular frequency (Larmor frequency) which is dependent on the strength of the magnetic field and on the properties of the specific nuclear species (the magnetogyric constant xcex3 of the nucleus). Nuclei which exhibit this phenomena are referred to herein as xe2x80x9cspinsxe2x80x9d.
While many different tissue samples and various bodies may be examined using NMR imaging, in order to further simplify this explanation the invention is described in the context of an exemplary transaxial volume through a patient""s body wherein the volume includes the patient""s heart and the volume will be referred to as a region of interest. In addition, it will be assumed that an NMR imaging system includes a three dimensional imaging area having Cartesian coordinate x, y and z axes and that the patient is positioned within the imaging area with the patient""s height (i.e. from head to feet) defining an axis along the z axis.
When the region of interest is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclear spins in the region attempt to align with the polarizing field, but precess about the direction of the field in random order at their characteristic angular or Larmor frequencies, producing a net magnetic moment Mz in the direction of the polarizing field.
If the region of interest is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment Mz may be xe2x80x9ctippedxe2x80x9d into the x-y plane to produce a net transverse magnetic moment which is rotating or spinning in the xy plane at the Larmor frequency.
The NMR signal which is emitted by the excited spins after the excitation signal B1 is terminated is a function of physical properties of the spin which generates the signal. These emitted NMR signals are digitized and processed to generate an NMR data set.
To determine the point of origin of an NMR signal, each NMR signal is encoded with spatial information, such as by the xe2x80x9cspin-warpxe2x80x9d technique, discussed by W. A. Edelstein et al. in xe2x80x9cSpin Warp NMR Imaging and Applications to Human Whole-Body Imagingxe2x80x9d, Physics in Medicine and Biology, Vol. 25, pp. 751-756 (1980) which is incorporated herein by reference.
According to the spin-warp scheme, spatial encoding is accomplished by employing three magnetic gradient fields (Gx, Gy, and Gz) which have the same direction as polarizing field B0 and which have gradients along the x, y and z axes, respectively. By controlling the strength of these gradients during each NMR cycle, the spatial distribution of spin excitation can be controlled and the point of origin of the resulting NMR signals can be identified.
A useful acquisition technique is the slice or two dimensional technique wherein NMR data are acquired for a single transaxial slice of a region of interest at one time. The invention is described in the context of slice imaging wherein several slices are acquired consecutively and are xe2x80x9cstackedxe2x80x9d to form a three dimensional data set.
To determine the z-axis origin of a signal during slice data acquisition, signal generation is limited to a specific transaxial slice of the region of interest using gradient field Gz. To this end, the Larmor frequency F of a spin can be expressed as:
F=(B0+Bz)xcex3xe2x80x83xe2x80x83(1)
where Bz is essentially the strength of gradient Gz within a specific transaxial slice of the region of interest and is the magnetogyric constant of the nucleus of the material in which the field is generated. Because the gradient field strength varies along the z-axis, each z-axis slice has a different Larmor frequency F. When the excitation signal B0 is provided at a specific excitation frequency, only spins within the xe2x80x9cselectedxe2x80x9d z-axis slice which are at the excitation frequency are tipped. Therefore, when the excitation signal B0 is turned off, only spins within the selected z-axis slice generate NMR signals.
To spatially encode NMR signals along the x axis, excitation signal B0 is provided at a small range of frequencies. The x axis gradient Gx is small enough that all of the spins along the x axis have Larmor frequencies within the small range of excitation signal frequencies and therefore each of the spins along the x axis generates an NMR signal when the excitation signal is turned off, each x-axis signal having a unique and identifiable frequency. Hence, x-axis position can be determined by identifying the frequency of each NMR signal received during an acquisition. This type of encoding is commonly referred to as frequency encoding.
To encode y axis position within NMR signals, the y axis gradient Gy is employed to cause spins along the y axis to have different phases; therefore, resulting NMR signals from spins along the y axis have different phases which can be used to determine y axis position. Because y axis position is encoded using signal phase, this type of encoding is commonly referred to as phase encoding.
After data have been acquired for one region of interest slice, the acquisition process is repeated for adjacent region of interest slices until data have been acquired for every slice within the region of interest. After digitizing and processing, the slice data are combined to provide a three dimensional data point (TDDP) array. The TDDP array includes a plurality of data points distributed at regular parallelepiped positions in a three dimensional lattice within the region of interest, at least one value (Vxyz) being characteristic of a physical property of the region of interest associated with each respective one of the lattice positions. Each cubically adjacent set of eight such positions defines a cubic volume referred to hereinafter as a xe2x80x9cvoxelxe2x80x9d, a physical property value being specified for each of the eight voxel vertices.
After a complete TDDP array has been acquired and stored, the array can be used to form an image of the region of interest using one of many well known reconstruction techniques.
For the purposes of this explanation, signals which are generated by spins and are characteristic of the property of the region of interest being detected will be referred to as xe2x80x9ctruexe2x80x9d signals, signal components which are randomly generated within a region of interest will be referred to generally as xe2x80x9cnoisexe2x80x9d and the combination of true signals and noise will be referred to as a xe2x80x9ccombinedxe2x80x9d signal.
While extreme measures are taken when designing an NMR system to minimize stray and random magnetic fields and signals within the region of interest during a data acquisition period, noise often occurs in two forms: first, as a background distortion exhibiting a low and relatively constant amplitude throughout a region of interest, and second, with appreciable amplitude caused by localized magnetic fields within the region of interest. The latter type of noise, being localized, will be referred to hereinafter as xe2x80x9clocalized noisexe2x80x9d.
Unfortunately, extremely sensitive sensing coils required to detect low amplitude true signals also detect an appreciable amount of background noise from within the region of interest during an acquisition period. Therefore, after a data acquisition period, each TDDP array data point typically includes both a true signal component and a noise component (i.e each data point value constitutes a combined signal). In addition, some data points are dominated by a localized noise component.
While an image can be generated using combined signals, the noise components reduce image clarity and minimize diagnostic usefulness of the image. In addition, localized noise causes artifacts within a resulting image. For this reason, to the extent possible, noise must be eliminated from the TDDP array prior to generating an image therefrom.
Various filtering techniques have been devised for reducing image noise. These filtering techniques can generally be divided into two different types, thresholding and morphological filtering. According to an exemplary thresholding technique, each combined signal within the TDDP array is compared to a threshold value. The threshold value is selected such that, below the threshold value most signals are generally known to be dominated by a background noise component (i.e. the true signal component is relatively small). Where a combined signal value is less than the threshold value, the combined signal value is set equal to zero. Where a combined signal value is equal to or greater than the threshold value, the combined signal value is maintained in the TDDP array.
While thresholding eliminates isolated low amplitude noise (i.e. where the true signal component is relatively small compared to the noise component), such techniques fail to reduce noise within a combined signal where a true signal component is appreciable. In addition, thresholding techniques fail to eliminate localized noise where noise amplitude is relatively high.
Morphological filters may be categorized as either binary or gray level. Binary filters use an eroding and dilating protocol to reduce image noise. To this end, an exemplary binary filter first uses the thresholding technique to reduce background noise and generate a binary TDDP array. In the present context, binary indicates that any data point value above the threshold is set equal to a normalized one value while any data point value below the threshold value is set equal to zero. Next, with the binary array formed, an erosion process is performed on the array wherein structures within the array are identified, a structure being any one separate data point, or a set of two or more adjacent data points, each having a value of one. An exemplary structure may include a sphere which has a diameter of 100 points, each point within the sphere having a one value. To erode the array, data points which have one values and are associated with the outer boundaries of each structure are changed to zero values. In effect the xe2x80x9couter layerxe2x80x9d of each structure within the array is xe2x80x9cpeeledxe2x80x9d away. For example, after a signal erosion process, the spherical structure which initially had a diameter of 100 data points would have a diameter of 98 data points (i.e. the outer layer on both sides of the sphere is eliminated). In most embodiments several erosion steps are consecutively performed, thereby reducing the size of each structure within the array.
While most structures within the array are maintained throughout the erosion process, some structures are entirely eliminated. For example, small structures, such as a single data point having a one value, are eliminated during a first erosion process. During a second erosion process, a sphere initially having a four data point diameter would be eliminated, and so on. Such elimination is intended, as most such small structures are attributable to localized noise.
After the erosion process, the dilation process is performed on the eroded array. Dilation is the opposite of erosion and adds layers to each structure within an array instead of removing layers. For example, during dilation, where the spherical structure mentioned above includes a diameter of 96 data points after erosion, the sphere would have a diameter of 98 after a first dilation process, and the diameter would be 100 after a second dilation process, and so on.
After dilation the resulting binary array can be used to generate an image or, in the alternative, can be used as a mask to select sections of data from the initial TDDP array for generating an image.
In addition to eliminating background noise, the binary filter also eliminates free standing localized noise from the TDDP array and therefore is generally a better filtering option than simple thresholding. Unfortunately, like thresholding, binary filtering cannot eliminate noise components which are combined with true signals to form combined signals.
Gray level morphological filters reduce data point intensities to minimize noise. Thus, for each data point in a TDDP array, a gray level filter compares the intensity of the data point and all surrounding data points in the TDDP array (e.g. above, below, left, right, front and behind) and replaces the data point intensity with the minimum intensity level of adjacent points. The resulting data point array includes minimal background noise and minimal localized noise throughout the entire array.
While gray level filters are advantageous, they can cause reduction in anatomical edge annunciation as resulting images have xe2x80x9csmearedxe2x80x9d gray levels (i.e. the gray scale contrast is reduced).
The above described filtering techniques have been combined in advantageous ways to reap benefits of each of the separate techniques. While filtered images have proven good enough for most diagnostic purposes there is always a desire to have better imaging techniques wherein the effects of noise are further eliminated without reducing the effects of true signals.
An exemplary embodiment of the invention includes a method for reducing noise in a three dimensional rectilinear parallelepiped data point array, the three dimensions being first, second and third dimensions and each data point associated with a point value. The method constitutes an erosion process for each array data point, wherein the data point is a point of interest, and comprises determining first, second and third erosion gradients through the point of interest along the first, second and third dimensions, respectively, and modifying the point of interest value as a function of the erosion gradients, thereby generating an updated point of interest value.
The method also constitutes a dilation process comprising, for each updated point of interest value, determining first, second and third dilation gradients through the updated point of interest along the first, second and third dimensions, respectively, and modifying the updated point of interest value as a function of the dilation gradients, thereby generating a revised point of interest value.
By using gradients to erode and then dilate TDDP array data point values, both background and localized noise can essentially be eliminated from a data set without appreciably deteriorating edges. In any event, images resulting from use of the inventive filter have better and more accurate characteristics than images generated using other filters.